A satellite for a satellite telecommunication system transmits signals at different powers on the downlink connection. The powers are chosen to limit the relative dynamic range of signals received on the downlink connection. The relative dynamic range of signals received on the downlink connection is advantageously less than 5 dB and preferably less than 2 dB. A digital processor circuit is used, together with an analog-digital converter, a circuit taking the fast Fourier transform of the converted signals, a circuit for monitoring the gain of the signals, a circuit for switching the signals to at least two amplifier subsystems each including an inverse fast Fourier transform circuit, a digital-analog converter and a power amplifier.